3(7u-v)(7u+v)=0

Solution for 3(7u-v)(7u+v)=0 equation:

Simplifying
3(7u + -1v)(7u + v) = 0

Multiply (7u + -1v) * (7u + v)
3(7u * (7u + v) + -1v * (7u + v)) = 0
3((7u * 7u + v * 7u) + -1v * (7u + v)) = 0

Reorder the terms:
3((7uv + 49u2) + -1v * (7u + v)) = 0
3((7uv + 49u2) + -1v * (7u + v)) = 0
3(7uv + 49u2 + (7u * -1v + v * -1v)) = 0
3(7uv + 49u2 + (-7uv + -1v2)) = 0

Reorder the terms:
3(7uv + -7uv + 49u2 + -1v2) = 0

Combine like terms: 7uv + -7uv = 0
3(0 + 49u2 + -1v2) = 0
3(49u2 + -1v2) = 0
(49u2 * 3 + -1v2 * 3) = 0
(147u2 + -3v2) = 0

Solving
147u2 + -3v2 = 0

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '3v2' to each side of the equation.
147u2 + -3v2 + 3v2 = 0 + 3v2

Combine like terms: -3v2 + 3v2 = 0
147u2 + 0 = 0 + 3v2
147u2 = 0 + 3v2
Remove the zero:
147u2 = 3v2

Divide each side by '147'.
u2 = 0.02040816327v2

Simplifying
u2 = 0.02040816327v2

Take the square root of each side:
u = {-0.142857143v, 0.142857143v}